"""simple docstring"""


import string

# frequency taken from https://en.wikipedia.org/wiki/Letter_frequency
a				={
    'E': 12.70,
    'T': 9.06,
    'A': 8.17,
    'O': 7.51,
    'I': 6.97,
    'N': 6.75,
    'S': 6.33,
    'H': 6.09,
    'R': 5.99,
    'D': 4.25,
    'L': 4.03,
    'C': 2.78,
    'U': 2.76,
    'M': 2.41,
    'W': 2.36,
    'F': 2.23,
    'G': 2.02,
    'Y': 1.97,
    'P': 1.93,
    'B': 1.29,
    'V': 0.98,
    'K': 0.77,
    'J': 0.15,
    'X': 0.15,
    'Q': 0.10,
    'Z': 0.07,
}
a				='ETAOINSHRDLCUMWFGYPBVKJXQZ'
a				='ABCDEFGHIJKLMNOPQRSTUVWXYZ'





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   dict[str, int]:




						'''simple docstring'''



						lowerCamelCase__   ={letter: 0 for letter in string.ascii_uppercase}
						for letter in message.upper():
												if letter in LETTERS:
																		letter_count[letter] += 1

						return letter_count





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   str:




						'''simple docstring'''



						return x[0]





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   str:




						'''simple docstring'''



						lowerCamelCase__   =get_letter_count(__lowerCAmelCase							)
						lowerCamelCase__   ={
						    freq: [] for letter, freq in letter_to_freq.items()
						}
						for letter in LETTERS:
												freq_to_letter[letter_to_freq[letter]].append(__lowerCAmelCase							)

						lowerCamelCase__   ={}

						for freq in freq_to_letter:
												freq_to_letter[freq].sort(key=ETAOIN.find  ,       reverse=__lowerCAmelCase							)
												lowerCamelCase__   ="".join(freq_to_letter[freq]							)

						lowerCamelCase__   =list(freq_to_letter_str.items()							)
						freq_pairs.sort(key=__lowerCAmelCase  ,       reverse=__lowerCAmelCase							)

						lowerCamelCase__   =[freq_pair[1] for freq_pair in freq_pairs]

						return "".join(__lowerCAmelCase							)





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   int:




						'''simple docstring'''



						lowerCamelCase__   =get_frequency_order(__lowerCAmelCase							)
						lowerCamelCase__   =0
						for common_letter in ETAOIN[:6]:
												if common_letter in freq_order[:6]:
																		match_score += 1

						for uncommon_letter in ETAOIN[-6:]:
												if uncommon_letter in freq_order[-6:]:
																		match_score += 1

						return match_score


if __name__ == "__main__":
	import doctest

	doctest.testmod()



"""simple docstring"""


from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase = False							)				->   list[float]:




						'''simple docstring'''



						if radian_mode:
												return [magnitude * cos(__lowerCAmelCase							), magnitude * sin(__lowerCAmelCase							)]
						return [magnitude * cos(radians(__lowerCAmelCase							)							), magnitude * sin(radians(__lowerCAmelCase							)							)]





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase = 10**-1							)				->   bool:




						'''simple docstring'''



						lowerCamelCase__   =cross(__lowerCAmelCase  ,       __lowerCAmelCase							)
						lowerCamelCase__   =sum(__lowerCAmelCase							)
						return abs(__lowerCAmelCase							) < eps


if __name__ == "__main__":
	# Test to check if it works
	a				=array(
	    [
	        polar_force(718.4, 180 - 30),
	        polar_force(879.54, 45),
	        polar_force(100, -90),
	    ]
	)

	a				=array([[0, 0], [0, 0], [0, 0]])

	assert in_static_equilibrium(forces, location)

	# Problem 1 in image_data/2D_problems.jpg
	a				=array(
	    [
	        polar_force(30 * 9.81, 15),
	        polar_force(215, 180 - 45),
	        polar_force(264, 90 - 30),
	    ]
	)

	a				=array([[0, 0], [0, 0], [0, 0]])

	assert in_static_equilibrium(forces, location)

	# Problem in image_data/2D_problems_1.jpg
	a				=array([[0, -2000], [0, -1200], [0, 1_5600], [0, -1_2400]])

	a				=array([[0, 0], [6, 0], [10, 0], [12, 0]])

	assert in_static_equilibrium(forces, location)

	import doctest

	doctest.testmod()


